We note that the best performance with the separation approach at each channel SNR requires choosing the right constellation size.
Increasing the constellation order effectively increases the transmission rate.
However, while the increase in the transmission rate increases the quality of the compressed image, this will also increase the error probability over the channel.
Hence, we should choose the right constellation size for each channel SNR.
On the other hand, for DeepJSCC-Q, given an SNR, the higher the constellation order, the better the end-to-end performance.
This can be understood from the perspective of quantization error.
A higher order modulation essentially corresponds to greater number of quantization levels of the encoder output \(\mathbf {z} = f_{\theta }(\mathbf {x})\) , and thus a greater accuracy of \(\bar{\mathbf {z}}\)  in representing \(\mathbf {z}\) .
Since DeepJSCC has already been shown to surpass the performance of BPG and LDPC codes by [1]}, naturally, as we increase the constellation order, the performance of DeepJSCC-Q will approach that of DeepJSCC.
This is also why DeepJSCC-Q with 4096-QAM constellation performs better than 64-QAM in Fig. REF  for \(\text{SNR} > 7\) , even when the 4096-QAM model was trained for a higher SNR than the 64-QAM model.
